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The semigroup of not bijective finite selfmaps of an infinite set. (English) Zbl 0821.03030
From the introduction: Bjarni Jońsson presented an axiomatization of the semigroup of finite selfmaps of an infinite set. This semigroup arises concretely in universal algebra and algebraic logic as the semigroup of simultaneous variable substitution in finite argument functions. However, any simultaneous variable substitution can be synthesized from individual substitutions (these are not bijective), a possibility which corresponds abstractly to every finite selfmap being induced on every finite subset by some not bijective one. The goal could therefore be attained by axiomatizing just the not bijective finite selfmaps, which is accomplished here.
Reviewer: L.Esakia (Tbilisi)

03G99 Algebraic logic
08A99 Algebraic structures
20M20 Semigroups of transformations, relations, partitions, etc.
Full Text: DOI
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